The depth formula was first studied by Auslander [1]}. Suppose that \(\mbox{Pd}\,_R(M)<\infty \)  and that \(q\)  is
the largest integer such that \(\mbox{Tor}\,_q^R(M,N)\)  is nonzero. Auslander proved that if or \(\mbox{depth}\,_R(\mbox{Tor}\,_q^R(M,N))\le 1\)  either \(q=0\) , then the formula
\(\mbox{depth}\,_R(M)+\mbox{depth}\,_R(N)=\mbox{depth}\,R+\mbox{depth}\,_R(\mbox{Tor}\,_q^R(M,N))-q\) 
